How do you factor the expression # 15x^2 - 33x - 5#?

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Answer 1 · 2016-06-01T17:44:02

This equation does not have simple factor-able terms

#15*(-5)=75# we need factors of #-75# which sum to #-33#.

#(-15)*(5)=75# and #5-15=-10# No

#(-3)*(25)=75# and #25-3=22# No

#(-1)*(75)=75# and #75-1=74# No

#(15)*(-5)=75# and #-5+15=10# No

#(3)*(-25)=75# and #-25+3=-22# No

#(1)*(-75)=75# and #-75+1=-74# No

This expression is NOT simple factor-able.

We can check Quadratic equation
#x_1, x_2 = (-b/{2a}) pm sqrt{b^2 - 4ac}/{2a}#

#x_1, x_2 = (-(-33)/{2*15}) pm sqrt{(-33)^2 - 4*15*(-5)}/{2*15}#

#x_1, x_2 = 33/{30} pm sqrt{1089 + 60/{30}#

#x_1, x_2 = 33/{30} pm sqrt{1149/{30}#

#x_1, x_2 =2.22989675, -0.02989675#

Clearly this equation does not have simple factor-able terms